Question

Six angles of a convex octagon is congruent. Each of the two remaining angles is 20 degrees more than one of the other six angles. Find the measure of EACH angle.

Answer 1

Determine the sum of angles of octagon.

`\begin{gathered} S=(n-2)*180 \\ =(8-2)*180 \\ =6\cdot180 \\ =1080 \end{gathered}`

Let measure of each angle of six congurent angle be x.

Then measure of each of other two remaining angle is (x + 20).

Determine the value of x by using the sum of angles of octagon.

`\begin{gathered} x+x+x+x+x+x+x+20+x+20=1080 \\ 8x=1080-40 \\ x=(1040)/(8) \\ =130 \end{gathered}`

So measure of each angle of six congurent angle is 130 degree.

Determine the measure of two remaining angles.

`\begin{gathered} x+20=130+20 \\ =150 \end{gathered}`

Thus measure of angles of octagone are,

Six angle measure 130 degree each and two angle measure 150 degree each.

`130,130,130,130,130,130,150,150`